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rs to incorporate credit concentration risk into their evaluation of bank insolvency risk. I. Introduction ? Banks will be allowed to use their own internal models, such as CreditMetrics and Credit Risk+ and KMV39。s Portfolio Manager, to calculate their capital requirements against insolvency risk from excessive loan concentrations. ? The National Association of Insurance Commissioners (NAIC) has developed limits for different types of assets and borrowers in insurers39。P, Moody39。s capital to a particular sector. If it is estimated that the amount lost per dollar of defaulted loans in this sector is 50 cents, then the maximum loans to a single borrower as a percent of capital, defined as the concentration limit, is II. Simple Models of Loan Concentration Risk ? Concentration limit = Maximum loss as a ? percent of capital * (1/Loss ? rate) ? = 10% * [1/.5 ] ? = 20% ? Bank regulators in recent years have limited loan concentrations to individual borrowers to a maximum of 10 percent of a bank39。s cost of funds The expected loss on the loan [E(Li)]. ? [E(Li)] = The Expected Loss = (The expected probability of the borrower defaulting over the next year or its expected default frequency (EDFi)) * (The amount lost by the FI if the borrower defaults [the loss given default or LGDi]). III. Loan Portfolio Diversification and Modern Portfolio Theory (MPT) ? Return on the Loan (Ri): ? Measured by the socalled annual allinspread (AIS), which measures annual fees earned on the loan by the FI plus the annual spread between the loan rate paid by the borrower and the FI39。s default rate (?Di) around its expected value times the amount lost given default (LGDi). ? The product of the volatility of the default rate and the LGD is called the unexpected loss on the loan (ULi) and is a measure of the loan39。 then defaults are binomially distributed, and the standard deviation of the default rate for the ith borrower (?Di) is equal to the square root of the probability of default times 1 minus the probability of default [( EDF) * (1EDF)]1/2. III. Loan Portfolio Diversification and Modern Portfolio Theory (MPT) ? Correlation of Loan Defaults (?ij): ? To measure the unobservable default risk correlation between any two borrowers, the KMV Portfolio Manager model uses the systematic return ponents of the